Those who delve deep into AE [Austrian Economics] sooner or later find that its Tree of Knowledge needs to be pruned, because some nonsense has been grafted onto it. Rothbard, for example devoted some time to sawing off the Free Banking absurdity. This article will hack away at the Performative Contradiction Argument [applied to the Action Axiom], refuting it five different ways.
Devil’s Advocate: What’s the Performative Contradiction Argument, Dave?
Smiling Dave: It’s a clever seeming one line proof of the Action Axiom, which asserts that humans “act”, meaning do stuff with a goal in mind. It goes like this. Say Jones writes out a proof that humans do not act. Well now, he wrote that proof with a goal in mind, didn’t he?
DA: Sure did, his goal was to disprove the Action Axiom.
SD: Which means he Acted. Any attempt to prove humans do not act can only be laid out by acting. His deeds contradict his very proof. That’s what we call a performative contradiction. The very attempt to disprove the Action Axiom is itself an Action. You want to show humans do not Act by Acting. Performative Contradiction.
DA: Why is it called a performative contradiction and not just a contradiction.
SD: Because Philosophy nowadays has accepted Mathematics, Euclid if you will. In Math a contradiction means the argument presented is internally inconsistent. For example, say Kurt Godel wants to prove 2+2 =5. He gives the following argument
- We know 1+1= 2
- But 1+1=3 also.
- Add those two equations and get 2+2=5.
DA: Clever, but 1+1 cannot be both 2 and 3. Your first assertion and your second contradict each other.
SD: Exactly. That’s what is called a contradiction nowadays. A performative contradiction is a completely different animal. It grants that there is no internal contradiction in the proof, but introduces the human factor, the guy sitting down at his desk writing the proof. His actions contradict his proof. His very attempt to prove humans do not act actually proves that humans do act.
DA: Who thought up that method of contradiction?
SD: The same guy who made the following argument:
- A left glove and right glove are not the same, but we cannot pin down why they are different.
- Therefor, space and time and causality are not real things. They are just illusions in our head.
DA: Let’s move on. Why do you think the performative contradiction proof that humans act is flawed?
SD: There are five huge flaws, each one by itself enough to destroy the performative contradiction argument. First, it claims to prove a generality while actually only proving a particular instance. Second, it assumes you need a human to prove things. Third, it assumes that True and Provable are the same thing, which they aren’t. Fourth, it forgot about the 99% and the 1%. Fifth,it pretends a mere hypothetical case actually happened.
DA: Would you elaborate, please?
First Flaw. Thinking one case proves all cases.
SD: Sure. The first flaw is that it only proves one thing while claiming to prove an infinity of things.
To see this clearly, imagine an insane asylum where all the people in it have brain damage such that they are incapable of logical thinking. These poor people can only do things at random, to no purpose. But there is one guy in that place who is a little better off. He had one interval of sanity in all his life. And wouldn’t you know it, in that one interval he wrote out a perfect proof that humans do not act.
DA: Ha! He himself acted when he wrote that proof. Performative contradiction! He has shown that he acts. QED!
SD: Has he shown that he acts always, or even most of the time, or even twice?
DA: Of course not. The poor fellow is brain damaged. He only acted once.
SD: Has he shown that the other inmates act?
DA: Of course not. How can he? They are all nuts.
SD: But doesn’t the fact that he acted one single time prove that he always acts, and that all the other inmates always act?
DA: Dave, you are losing it. That’s like making the following argument.
- One day, Babe Ruth hit a home run that flew 600 feet.
- Therefor, Babe Ruth spends every waking moment hitting 600 foot home runs.
- Not only that, everyone spends every waking moment hitting 600 foot home runs.
SD: Exactly. This performative contradiction nonsense, even if we grant for the moment that it is a valid proof, proves only one home run. But it claims to prove an infinity of home runs, from the beginning of time to all eternity.
DA: But Dave, isn’t that how inductive proofs work? You see one instance, and you generalize.
SD: Inductive reasoning needs more than one instance to get started.
DA: OK, I think we get the first flaw. What’s the second flaw?
Second Flaw. Assuming you need a human to prove things.
SD: To understand this flaw, consider for a moment the equation 2+2=4. Let us imagine the situation before man walked the Earth. Was 2+2 equal to 5 back then? Does the presence or absence of humans change the nature of Mathematics?
DA: Dave, there are some philosophers who claim Math is all an invention in ones head. That until some living human actually thought of it, 2+2 did not equal 4, or any other number.
SD: More power to them, but there are plenty of others who think that 2+2=4 is a fact of nature. There are trees, and there are oceans, and there are mathematical truths, all equally “real” and independent of human existence.
DA: Yes, that’s the common sense approach, I grant you. It definitely has not been proven wrong by anyone, the guy who couldn’t tell his left glove from his right notwithstanding. But where are you going with this?
SD: If we claim that 2+2=4 even when no men are alive, that Arithmatic “exists” even before someone writes it down on paper, so too we can claim that valid proofs “exist” even though no one has written them down.
DA: Ah, but you cannot prove that, Dave.
SD: But I don’t have to. Let’s remember what we are talking about. Smith publishes a proof that human do not act. Jones says Smith has made a performative contradiction by writing the proof down, and that this somehow invalidates Smith’s proof. But surely that’s a non sequitur, unless Jones is assuming that a proof has to be written down, and that the proof has no existence until it is written.
In other words, Jones is assuming, with no proof, that 2+2 is not equal to 4 until someone writes it down. The burden of proof is on Smith to prove that absurd notion.
DA: Dave, you’ve got my head spinning. Can you dumb it down a little?
SD: OK, until now I have claimed that a proof is a proof even before anyone writes it down. If that is over your head, Devil, I’ll change the argument just a little. I claim that a proof is a proof even if a non human writes it down. Certainly once it’s on paper, it’s a proof, we can all agree, no matter who wrote it.
DA: I see where you are going with this. The Performative Contradiction Argument is that the human who tries to prove that Humans do not Act is acting when he writes down the proof. But if a non-human writes the proof, there is no contradiction. A non-human has acted when writing down the proof, which does not contradict the claim that Humans do not act.
SD: Precisely.
DA: What I don’t get is, what non human could write down that proof? A cow? A horse?
SD: There are plenty of possibilities. First of all, there is God. He could write the proof.
DA: But what if someone denies the existence of God?
SD: So the Performative Contradiction Argument, to be valid, will have to prove God does not exist. Good luck with that.
DA: You said there are many possibilities of non humans who could write down the proof. Who else?
SD: Ever heard of SETI?
DA: The Search for Extra-Terrestrial Intelligence. Sure. There are serious people, including Nobel Prize winning scientists, who think it very likely that there is intelligent life on other planets.
SD: Intelligent enough to write a proof?
DA: I see what you mean. So the Performative Contradiction Argument has to prove they don’t exist either. Who else could write the proof?
SD: Dolphins. Scientist believe that dolphins are as smart as humans. For now, they have not yet deciphered their language, even though they can hear it underwater. But one day they may, and lo and behold the first thing they tell us may well be a proof that Humans do not Act.
DA: So the Performative Contradiction Argument has to prove dolphins are stupid. Who else?
SD: The cows and horses you mocked earlier.
DA: What?
SD: Let me quote Wikipedia:
The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type any given text, such as the complete works of William Shakespeare. In fact, the monkey would almost surely type every possible finite text an infinite number of times. However, the probability that monkeys filling the observable universe would type a complete work such as Shakespeare’s Hamlet is so tiny that the chance of it occurring during a period of time hundreds of thousands of orders of magnitude longer than the age of the universe is extremely low (but technically not zero).
DA: So a cow or horse or a monkey doodling with his paw on the ground may wind up writing a proof that Humans don’t Act. But the probability of that is extremely low, Dave.
SD: But not zero. The Performative Contradiction Argument doesn’t say a proof that Humans do not act is unlikely to be found. He claims it cannot possibly be be found. Well it can.
DA: So the Performative Contradiction Argument forgot about God, about Martians, about dolphins, and about monkeys typing away.
SD: And also about Nobody. Our original argument is that a proof is a proof even if nobody writes it down. What I’m saying may sound amusing, what with Martians and monkeys, but if you examine it closely you see it refutes the Performative Contradiction Argument decisively. And I didn’t even get to parrots, or the inmates of that insane asylum we mentioned earlier.
DA: No need, Dave, we get the idea.
SD: Summing up, the Performative Contradiction Argument is as follows:
- Every proof has to be written down by a Human.
- But the Human who wrote it down had a goal in mind, i.e he Acted.
- Therefor all Humans Act, at least most of the time.
The first flaw is that 3. is a non sequitur. It does not follow from 1. and 2., as we have shown.
The second flaw is that 1. is false, as we have shown. And so is 2., for that matter. [Maybe the human who wrote the proof was insane and lobotomized and could only type things with no purpose in mind.]
DA: You’ve shot down the Performative Contradiction Argument by exposing two huge flaws, each one by itself enough to leave it dead in the water. What’s the third flaw?
Third Flaw: Confusing True and Provable.
SD: To understand the third flaw, let’s look at the Axiom of Choice. Godel proved that it cannot be proven false. So for a couple of years, mathematicians considered it true.
DA: Just like the Action Axiom. If we accept, for the sake of argument, that the Action Axiom cannot be proven false, then we have proven, or at least we can assume, that it is true.
SD: Yes, that was the situation for a while. But then Paul Cohen proved that the Axiom of Choice cannot be proven true either.
DA: You mean it cannot be proven true, and also cannot be proven false?
SD: Sounds crazy, no? But that’s the situation. Just because something cannot be proven false, that does not mean it is true. So this whole use of the Performative Contradiction Argument has been obsolete for a good fifty years. I’ve seen it used by people to prove all kinds of things. How wrong they are.
DA: And that’s the third flaw, thinking Unprovable means False.
SD: Yep.
DA: But what about the Law of the Excluded Middle? Is that wrong, too?
SD: No, it’s still correct that any assertion is either true, or it’s negation is true. But again, let us not confuse true with provable. An assertion may be true, but neither it nor it’s negation may be provable. In Math alone, there are an infinity of such assertions, as Godel proved.
DA: So bottom line, even if we ignore the two previous flaws [for the sake of argument] in the Performative Contradiction Argument, there is still a problem with it. It proves something, but not what it claims to prove.
SD: Yes. It proves that the negation of the Action Axiom is unprovable, but it claims to prove more, that the Action Axiom is true. Big Mistake.
DA: On to the fourth mistake
Fourth Mistake: It forgot about the 99% and the 1%..
SD: This one is very simple. Say a person proves that humans do not act 99% of the time. That’s enough to destroy the underpinnings of AE. But there’s no performative contradiction. He proved humans do not act 99% of the time. His action of writing out the proof belongs to that 1%.
DA: Like if a rich man claims 99% of the world is poor, yet he is rich. No contradiction there.
SD: Yep.
DA: But Dave, isn’t this the same as the first flaw, which is trying to prove the universal from a single particular case?
SD: The difference is this. The first flaw talks about Jones trying to prove all humans do not act, and claiming it proves all humans do act. This fourth flaw points out that with a slight modification of what Jones is trying to prove, that AE can be destroyed.
DA: So the first flaw is talking about Jones trying to prove all humans never act, and this new flaw talks about Jones trying to prove most humans do not act most of the time.
What’s the fifth blunder?
Fifth flaw: Pretending the hypothetical actually happened.
SD: To show this flaw in all its absurdity, I will now prove that Julius Caesar is alive today.
- If Julius Caesar were to claim today that he is dead, that would prove he is alive today.
- Thus any attempt by Caesar to prove he is dead today is a performative contradiction
- Therefor Julius Caesar is alive today.
DA: Now wait just a minute, Dave. Caesar never actually got up today and said he is alive. You are taking a hypothetical situation and pretending it actually happened.
SD: Which is exactly the same mistake the performative contradiction argument makes. It talks about a hypothetical, someone writing out a proof that humans do not act, pretends it actually happened, and concludes that a performative contradiction actually happened.
DA: But maybe it doesn’t do that, Dave. Maybe all it is saying is that the hypothetical case would lead, hypothetically, to a hypothetical performative contradiction, not that a perf. cont. actually happened.
SD: And that is proof enough that humans act?
DA: Ermm, yes.
SD: So I have proof enough that Julius Caesar is alive today, too.
DA: I see what you did there. Touche.
Summing up.
SD: Summing up, we have shown that the performative contradiction proof is a huge embarrassment to AE.
DA: Almost as embarrassing as thinking that the existence of left gloves proves there is no causality.
SD: And it is totally unnecessary, as we will show in what follows.
What did Mises think about this whole thing?
DA: You wrote earlier that the Performative Contradiction Argument is a graft onto the Tree of Austrian Knowledge. But isn’t it part of the tree itself? Didn’t Mises believe in it? Doesn’t the Action Axiom stand or fall with the Performative Contradiction Argument?
SD: Not at all. In David Gordon’s An Austro-Libertarian View, Vol. I, he quotes a discussion between Israel Kirzner and Mises:
This writer [Kirzner] once asked Mises how a person can know that human beings other than himself are indeed purposeful… Mises answered my query by saying, in effect, that we become aware of the existence of other human agents through observation.
DA: Through observation. That’s how we know that other people act. [I guess we know that we ourselves act by introspection].
SD: Notice he didn’t say we know other people act because we can prove it using the old Performative Contradiction Argument.
DA: He was too smart for that.
SD: Yep.
Smiling Dave on Austrian Economics. 